Triple

T14265232
Position Surface form Disambiguated ID Type / Status
Subject Tarski–Mostowski–Robinson theorem E353626 entity
Predicate usesConcept P531 FINISHED
Object Łoś's theorem
Łoś's theorem is a fundamental result in model theory that characterizes the truth of first-order formulas in ultraproducts by showing they hold exactly when they are true in "almost all" component structures.
E1090229 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Łoś's theorem | Statement: [Tarski–Mostowski–Robinson theorem, usesConcept, Łoś's theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Łoś's theorem
Context triple: [Tarski–Mostowski–Robinson theorem, usesConcept, Łoś's theorem]
  • A. Halász theorem
    Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
  • B. Low’s theorem
    Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
  • C. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • D. Haag’s theorem
    Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
  • E. Kesten’s theorem
    Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Łoś's theorem
Triple: [Tarski–Mostowski–Robinson theorem, usesConcept, Łoś's theorem]
Generated description
Łoś's theorem is a fundamental result in model theory that characterizes the truth of first-order formulas in ultraproducts by showing they hold exactly when they are true in "almost all" component structures.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Łoś's theorem
Target entity description: Łoś's theorem is a fundamental result in model theory that characterizes the truth of first-order formulas in ultraproducts by showing they hold exactly when they are true in "almost all" component structures.
  • A. Halász theorem
    Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
  • B. Low’s theorem
    Low’s theorem is a result in quantum electrodynamics that constrains the behavior of scattering amplitudes involving the emission of low-energy (soft) photons.
  • C. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • D. Haag’s theorem
    Haag’s theorem is a result in axiomatic quantum field theory showing that the interaction picture cannot be consistently defined for interacting fields in the same Hilbert space as free fields, undermining the standard formulation of quantum field theory.
  • E. Kesten’s theorem
    Kesten’s theorem is a fundamental result in probability theory that characterizes when a random walk on a group is transient or recurrent, with deep implications for random walks on groups and percolation theory.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d8278c43e08190824146f4632b89a5 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de6357a8188190ba518a486521052b completed April 14, 2026, 3:55 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd326551b08190ae8fe220a6422339 completed May 8, 2026, 12:46 a.m.
NEDg Description generation batch_69fd3417e8e88190b099bfe4ba30f364 completed May 8, 2026, 12:53 a.m.
NED2 Entity disambiguation (via description) batch_69fd37df3dfc8190a594abb2c14e11bb completed May 8, 2026, 1:09 a.m.
Created at: April 10, 2026, 1:09 a.m.